What is the derivative of SEC(x)?

The correct answer to this question is secxtanx. There are two ways to find this derivative. The first way is to limit the derivative's definition or use the definition of the secant itself.

This is sec x = 1 cos x. We must also keep in the back of our mind the equation d x cos x = − sin x. From there, we can take several different steps to solve the derivative, as well as many mathematician rules like the quotient rule.

In the end, the derivative is solved with d d x sec x = d d x 1 cos x = sec x tan x